I don't know them both at all well but we did visit them on out last trip to the UK so from a tourists eye......
I actually found Stratford to be a more relaxing place to walk about in compared to Cheltenham....maybe it was the river. Should be said it wasn't high season so it was probably quieter than I imagine it normally would be. Cheltenham is nice but the day we were there it was rather busy so I didn't find it particularly relaxing.....although the wife enjoyed the shops.